Capacity approaching codes for photon counting receivers

In [1] a low-complexity photon-counting receiver has been presented, which may be employed for weak-energy optical communications and which is typically modeled through its equivalent Binary Symmetric Channel (BSC) model. In this paper we consider the scheme described in [1], we model it as a time varying Binary Input-Multiple Output (BIMO) channel and analyze its performance in presence of soft-metric based capacity approaching iteratively decoded error correcting codes, and in particular using soft-metric based Low Density Parity Check (LDPC) codes. To take full advantage of such detector, soft information is generated in the form of Log-Likelihood Ratios (LLRs), achieving reduction in Bit Error Rate (BER) and Frame Error Rate (FER) with respect to classical BSC and Additive White Gaussian Noise (AWGN) channel models. Furthermore, we explore the limits of the achievable performance gains when using photon counting detectors as compared to the case when such detectors are not available. To this end, we find the classical capacity of the considered BIMO channel, clearly showing the potential gains that photon counting detectors can provide in the context of a realistic cost-effective scheme from an implementation point of view. Furthermore, we show that from a channel modeling point of view, we can observe that the BIMO channel can be approximated with an AWGN channel for high values of mean photon count Nc, while the AWGN model offers an unreliable result with a low mean photon number Nc, (i.e. with low raw BER). This effect is more evident with lower coding rates.